Not a Cycle of Violence:

An Episodic Analysis of The Israel-Gaza Conflict

Alexei Abrahams∗, Eli Berman†, Prabin Khadka‡, Esteban F. Klor§, and John Powell¶

February 2018

Does violent retaliation of state and non-state actors to violent attacks lead to deterrence

or, on the contrary, to counter-retaliation and an increase in violence? This paper studies this

issue focusing on the Gaza-Israeli conflict between 2007 and 2014 using original security reports

from the United Nations. The data include all Palestinian projectile launches (over 16,000) and

Israeli airstrikes (over 8,800) during the period at issue down to the five-minute interval at which

the action occurred. Our findings argue against the importance of cyclical counter-retaliation as

driving this persistent conflict. First, this conflict is characterized by short-lived episodes of violence

separated by quiet interludes. Violent episodes tend to last less than one day and are followed by

three and a half days without attacks. Second, 61% of violent episodes include an initial attack

that doesn’t induce a retaliation, and among the ones that do, the median number of successive

counter-retaliations is only 3. Third, violent episodes are not themselves cyclically related: 91% of

violent episodes are initiated by Gazan militants attacks and 84.9% of violent episodes end with

a Gazan militant attack. Finally, we find no evidence that episodes with counter-retaliations (i.e.,

cycles of violence) induce or deter subsequent violence. The median number of days without attacks

after cycles of violence (3.1) is almost the same to the median number of days without attacks for

all episodes (3.4). Moreover, the type of projectile launched by Gazan militants does not seem to

be affected by Israeli retaliation or the lack thereof.

∗ Harvard University, Belfer Center - Middle East Initiative; alexei abrahams@alumni.brown.edu; † Department of

Economics, University of California at San Diego; elib@ucsd.edu;‡ Department of Politics, New York University; §

Department of Economics, The Hebrew University of Jerusalem; eklor@huji.ac.il; ¶ Harvard Kennedy School, Stan-

ford Graduate School of Business

1. Introduction

Whether by American drones bombing Al-Qaeda operatives in Yemen’s Hadramawt Desert, or

ISIS operatives spraying civilians with gunfire in downtown Paris, state and non-state actors are

regularly projecting violence across borders. This leads us to the main question of this paper:

How should state and non-state actors respond to violent attacks? For politician and policymakers

wishing to minimize future violence and/or seeking optimal strategies to ensure national security,

the same basic tradeoff arises. On the one hand, responding to attacks with reprisals can deter

future aggression by attaching a price tag (Schelling, 1966). On the other hand, there are many

other instances where reprisals have provoked deadly counter-reprisals or ‘blowback’ (Johnson,

2000).

The response to Hizbullah’s rocket attacks on northern Israel in the summer of 2006 is perhaps

the clearest demonstration of the deterrent logic of retaliation in recent history. The Israeli air force

(IAF) bombed southern Lebanon with cluster munitions, killing a substantial number of Hizbullah’s

soldiers while destroying bridges, roads, and other infrastructure. Though Hizbullah’s capacity to

inflict harm was not meaningfully diminished, they nonetheless became hesitant to launch further

attacks, and the two sides have remained in a peaceful equilibrium of mutual deterrence ever since

(Sobelman, 2017). On the contrary, Israel’s assassination of Hamas operative Yahya Ayyash in

January of 1996 is an example of retaliations leading to deadly counter-reprisals. Right after the

assassination Hamas observed forty days of mourning, and then carried out a series of retaliatory

suicide bombings that claimed the lives of 59 Israeli civilians (Ephron, 2015). Therefore, a clear

understanding of the deterrence-blowback tradeoff is critical for state and non-state actors that

want to avoid protracted cycles of violence.

Quantifying this tradeoff for a given context seems to be a problem well suited for social sci-

entists. Yet, preliminary efforts have so far reached contradictory conclusions. If the blowback

effect dominates, we should observe that violence follows a cyclical pattern, with reprisals giving

rise to counter-reprisals, and so on. In search of these cycles, studies have thus far focused on the

Israel-Palestine conflict, which makes sense for at least two reasons. First, among all contemporary

conflicts, the Israeli-Palestinian conflict is relatively self-contained, unlike the nebulous ‘war on ter-

ror’ waged between Western allies and groups like ISIS and Al-Qaeda. Second, among self-contained

conflicts, the Israeli-Palestinian conflict lends itself to statistical analysis via a consistently high

1

rate of violent incidents, in contrast to, say, the conflict between Israel and Hezbollah.

Not only have studies focused on the Israeli-Palestine conflict, but they have almost all relied on

a vector auto-regression (VAR) framework, which allows for causal feedback between actions and

reactions. Despite these commonalities, the results of these studies are at odds with each other.

Applying a VAR methodology to fatalities data from the Second Palestinian Uprising (2000-2005),

Jaeger and Paserman (2008) find that Israel retaliates against Palestinian attacks, but Palestinians

do not counter-retaliate. Haushofer et al. (2010) also apply a VAR framework to fatalities data

augmented with Palestinian rocket launch incidents. They find that both sides retaliate. Duggan

and Chenoweth (2012) run VAR-like regressions using different data, finding evidence that Pales-

tinians retaliate while Israeli actions are apparently unprovoked. Thus, despite using the same

methodology and restricting their focus to the Israeli-Palestinian conflict, the literature is far from

reaching a consensus on the deterrence-blowback tradeoff.

While the studies cited above use disaggregated daily data and standard econometric techniques,

we believe that the existing literature suffers from several shortcomings. The main empirical issue

is that all related studies rely on a VAR framework, which we argue may not be the appropriate

tool to establish the existence or not of cycles of violence. Whereas a VAR analysis may be helpful

to determine whether Israel retaliates to Palestinian violence, and Palestinians retaliate to Israeli

violence, the VAR analysis does not push the data far enough. While a VAR analysis allows us to

determine whether or not a protracted cycle of violence exists between the two sides, it still leaves

most of the important questions following a cycle of violence approach open: (i) How do cycles

start? (ii) How do they end? (iii) Does retaliation lead to escalation or de-escalation of violence?

and (iv) Are violent episodes linked to each other by a pattern of provocation and reprisal?

This paper addresses the questions above focusing on the protracted Gaza-Israeli conflict be-

tween 2007 and 2014. The analysis relies on daily original security reports from the United Nations

on violent incidents in the Gaza Strip between 2007 and 2014. These reports include all Palestinian

projectile launches (over 16,000) and Israeli airstrikes (over 8,800) during the period at issue down

to the five-minute interval at which the action occurred. We supplement these data with weekly

Israeli counter-terrorism reports (2009-2016). All told, our data span 111 months of conflict.

The available data allow us to cluster fluctuations on violence into violent episodes. Using a

subset of reprisals explicitly linked to earlier provocations, we find that it usually takes both sides

at most two days to retaliate to provocations. We use this upper bound to cluster violent incidents

2

into episodes, where episodes are separated from each other by at least two days of quiet.1 They

are thus unlikely to be related to each other in the sense of provocation-reprisal (for robustness, we

also create violent episodes using a longer threshold for days of quiet). We focus on these episodes

to analyze the observed patterns of attacks, retaliations, and counter-retaliations. We also analyze

how violent episodes start after periods of calm, escalate, de-escalate, and end.

The results of our analysis show that violent attacks between Israel and Gazan militants exhibit

an episodic pattern consisting of brief projectiles and airstrikes skirmishes lasting one day, and

separated by over three days of quiet. Over 90% of these episodes of violence are started by

Gazan militants and almost 85% of them are ended with a Gazan militants’ attack. In fact, in

58.7% of violent episodes only Gazan militants commit attacks. Israel tends to be patient on its

retaliation policy, and tends to wait for five or more projectiles attacks before retaliating (if at

all). On the contrary, Gazan militants retaliate to Israeli airstrikes right after one or two attacks.

Whereas a VAR analysis would lead us to believe that both sides are trapped in a protracted cycle

of violence, our episodic analysis shows that less than 30% of violent episodes actually constitute

cycles of violence, in the sense that they include an attack, a retaliation and a counter-retaliation.

Cyclical episodes are more violent (in terms of number of attacks) and last longer than non-violent

episodes. Interestingly, cyclical episodes (which include Israeli retaliations) do not seem to deter

future violence. The median number of days without attacks after an episode is almost the same

for cyclical and non-cyclical episodes. Moreover, the type of projectile launched by Gazan militants

in any given attack (mortars, Qassam rockets or Grad Rockets) does not seem to be affected by

Israeli retaliation (or the lack thereof).2

This research project, based on a careful analysis of two new data sources (which provide

unprecedented detail on up to the minute incidents previously unrecorded) presents an alternative

approach to study the pattern of violence in protracted conflicts. It focuses on violent episodes

as well as on periods of calm to study who initiates violent episodes, what leads these episodes

1This methodology is similar to clustering using the “nearest neighbor search,” which is common in computer

science. See, for example, Knuth (1973).2Mortars are indirect devices that launch projectiles to short ranges, which usually explode on open fields of

kibutzim surrounding the Gaza Strip. Qassam rockets have a longer range, up to 16km, and affect cities bordering the

Gaza Strip. Finally, Grad and Katyusha rockets can reach cities over 50km away from the Gaza Strip, like Southern

Jerusalem and Tel Aviv. Israel relates to the firing of projectiles with a longer reach against more populated cities

as an escalation in the level of violence.

3

to cycles of violence, and what brings these cycles to an end. This analysis complements previous

studies of the Israeli-Palestinian conflict using VAR analyses.3 Whereas VAR analyses tend to show

that both sides retaliate to violence, the episodic analysis of this paper clarifies how violent attacks

unfold within and between violent episodes.

Overall, this paper highlights a new type of analysis for protracted violent conflicts between

state and non-state actors that has been ignored in the literature on political conflict. We hope

that the insights of this study will provide a better understanding of protracted conflicts and their

patterns of violence, and lead to policy recommendations conducive to truces for violent conflicts

in the Middle East as well as for other protracted conflicts around the world. In addition, we hope

that paper will lead by example, encouraging researchers studying political conflict to investigate

time series data more creatively instead of directly applying off-the-shelf statistical methods like

VAR.

2. Data

Our analysis relies on high frequency original data from the United Nations. This data set consists

of daily security reports of notable violent incidents in the Gaza Strip recorded by UN observer

teams dating from October 2006 through December 2014. We begin analyzing the UN reports

on June 15th, 2007, the date on which the Islamic Resistance Movement (Hamas) seized control

of the Gaza Strip from Fatah security forces. The original reports are stored in MS Word files.

We batch-convert these to OpenOffice files, then import their text content to Python and exploit

formatting regularities to extract the date, timestamp, and location of every single violent incident

mentioned in the reports. Figure A1 in the appendix exemplifies a flowchart of data generation for

two incidents on June 25th, 2007.

The reports typically summarize each incident in two or three sentences. We exploit contextual

knowledge and verb patterns to write a Python grammar parser that extracts the attacker, target,

type and quantity of munition, and casualties associated with each violent action. Figure A2 in the

appendix illustrates how the grammar parser works using as examples two events that occurred on

August 17th, 2010. We cross-validate these data with daily human-coded aggregations of the same

3In addition to the studies cited above, see Jaeger and Paserman (2006; 2009) for another two prominent studies

of the Israeli-Palestinian conflict using a VAR-style framework.

4

reports, finding a 99% correlation for daily projectile tallies fired from Gaza towards Israel, and a

98% correlation for daily airstrike tallies fired by the Israeli Air Force (IAF).4

Figure 1 presents the daily tallies of IAF’s airstrikes and Gazans’ projectiles using UN data.

There are a total of 8,653 airstrikes and 16,473 projectiles fired between October 2006 and December

2014. This shows the high level of violence prevalent during this period. Out of 2,740 days included

in our sample, Gazan militants fired at least one projectile in 46.8% of them (for a total of 1,283

days with Gazan violence) and the IAF carried out at least one airstrike in 18.4% of them (for a

total of 504 days with an Israeli airstrike).

These numbers mask the great deal of variation on the level of violence over time. This pattern is

clearly depicted in Figure 1. The figure shows a relatively low number of daily attacks, together with

extremely violent periods occurring right before and during major violent confrontations between

Israel and Hamas. These include several major Israeli military operations, most notably Operation

Cast Lead (December 27th, 2008 until January 18th, 2009), Operation Pillar of Defense (November

14th, 2012 until November 21st, 2012) and Operation Protective Edge (June 12th, 2014 until August

26th, 2014). The figure makes evident that Gazan violence is more evenly distributed over time,

whereas Israeli violence substantially increases during its military operations. This figure also shows

that the overall level of violence substantially decreases after those operations vis-a-vis the level of

violence before the operations.

We complement the available UN data with weekly counter-terrorism reports on the Gaza Strip

compiled by The Meir Amit Intelligence and Terrorism Information Center, an Israeli think tank.

The Meir Amit’s reports on the Gaza Strip date back to April 15th 2009.5 The Meir Amit reports

are compiled by Israeli staff who are obviously not on the ground in The Gaza Strip. As a result,

their reports are not nearly as comprehensive as those compiled by the UN ground teams, and

are particularly poor when documenting major military operations. On the other hand, Meir

Amit reports draw on the IAF’s twitter feed, other social media sources, and official websites of

Palestinian militant groups to confirm, whenever possible, the main motive behind each violent

action. We human-code each violent incident recorded in these reports.

4During the period at issue Gazan militants fired mortars and rockets towards Israel. Our data set contains

detailed information on the type of weapon fired, and we use that information in our empirical analysis. In the text

of this paper, for brevity’s sake, we use the word ‘projectiles’ to refer to mortars or rockets.5These reports are freely accessible at http://www.terrorism-info.org.il/. Our analysis includes all the reports

between April 15th, 2009 until July 1st, 2016.

5

Using Meir Amit data we identify 303 Israeli airstrikes and 26 Palestinian projectiles launches

as reprisals explicitly linked to earlier recorded provocations. These figures represent 85.8% of all

Israeli airstrikes and 4.0% of all Palestinian projectile launches recorded in the Meir Amit data. The

substantial difference in terms of reprisals (85.8% versus 4.0%) could well be driven by reporting

bias: Meir Amit is based in Israel and is partly staffed by Israeli army veterans, which may lead

them to follow more feeds from Israeli sources than Palestinian sources. With that caveat in mind,

we use Meir Amit data in the body of this paper to calculate the typical delay in carrying out a

reprisal attack.

As Figures 2 and 3 suggest, both Israelis and Gazans tend to retaliate within one or two days

of the initial attack, with few exceptions. The speediness of retaliations makes sense for at least

two reasons. First, both sides have the technological capability to retaliate within hours of an

attack. Israel keeps fighter-jets ready to scramble. It also has drones in the skies over Gaza

which, according to our data, oftentimes spot and strike militant rocket crews even while they are

setting up to launch. Similarly, as already established by Haushofer et al. (2010), the technology

for launching mortars and rockets allows Gazan militants to carry out retaliations within hours

of provocation.6 Secondly, apropos the deterrence-blowback tradeoff, each side wants the other

to interpret its retaliation as a reprisal, i.e. as a price of the earlier provocation. Performing

retaliations soon after a provocation helps establish this causal linkage in the minds of internal

and external audiences. If for some reason the reprisal is delayed, the actor has added incentive

to announce publicly that this is a reprisal for the earlier provocation, thus raising the probability

that Meir Amit records it as such. We should therefore expect that our data on retaliation delays

is, if anything, biased upward by this selection issue.

6This contrasts with suicide attacks launched from the West Bank during the Second Intifada, which potentially

required weeks of planning [see Jaeger and Paserman (2008) and Brym and Araj (2006)].

6

3. Episodic Aggregation of Violent Attacks

We define a violent episode as any series of projectile launches or airstrikes preceded and followed

by at least t days of calm.7 Table 1 presents our analysis of episodic violence using the UN data.8

Following the evidence in Figures 2 and 3, Columns (1) and (2) define episodes of violence using

the threshold of at least two days of calm. Columns (3)-(4) and (5)-(6) present robustness tests

using at least 7 or 14 days of calm as the relevant thresholds, respectively. Odd numbered columns

in Table 1 take into account all projectiles launched by Gazan militants; that is, 5,189 mortars and

11,284 rockets. Even numbered columns focus exclusively on rockets launched and exclude mortars.

We do so because, due to their short range and poor precision, most mortars explode on empty

agricultural fields surrounding The Gaza Strip. Therefore, one may claim that the majority of the

Israeli public is less affected by these types of projectiles, and the IAF is less prone to retaliate to

these types of attacks.9

Let us focus first on Column (1) of Table 1, which depicts episodes’ characteristics using a ‘two

days of calm’ threshold. Using this threshold, we observe 312 episodes of violence. Panel A shows

that most violent episodes are short lived, with over 50% of them lasting less than 24 hours, and

over 75% of them lasting less than 4 days. As shown below, violent episodes lasting less than one

day consist mostly of projectile launches from Gaza without an Israeli retaliation. There are a few

violent episodes that continue for a long time. For example, the violent episode with the longest

duration lasted 129.8 days. This episode started on January 23rd, 2008 and ended on June 6th of

the same year. This episode showcases the sustained and high levels of violence that characterize

this conflict before Operation Cast Lead, which started the last week of 2008 and lasted for three

weeks (see also Figure 1).

Panel B shows that Gazan militants initiate 91% of violent episodes. Gazan militants also tend

to end violent episodes, as they launch the last attack in 84.9% of violent episodes. This provides

strong evidence that episodes are not related to each other cyclically. If they were cyclically related,

7Hamas denotes these short periods of calm with the Arabic term tahdiya. This contrast with longer and formal

ceasefires, which are called hudna.8All our analyses and results are consistent when using the Meir Amit data. We relegate those results to the

appendix because, as mentioned above, The Meir Amit data set is less reliable than the available UN data.9Note, however, that several studies show that mortar attacks are associated with localized increases on mis-

carriages (Wainstock et al., 2013), post-traumatic stress disorder (Diamond et al., 2010; Berger et al., 2012), and

depression (Goldberg et al. 2013).

7

we would expect that the side fired upon last in a given episode would be the first to fire in the

next episode. Instead, we find that Gazan militants overwhelming start and end exchanges of fire.

Moreover, we also observe that in 58.7% of all episodes projectiles launched from the Gaza Strip

go unanswered by Israel. If we add to that the episodes with only Israeli violence, we obtain that

60.9% of all violent episodes do not constitute cycles of violence because only one side commits

violent attacks.

Panels C and D presents summary statistics for the intensity of the attacks. The message

that emerges from these panels is consistent with the one obtained in Figure 1. Most days are

characterized by low levels of violence consisting of at most 2 projectiles launched from Gaza

without an Israeli retaliation (for 75% of the days in our sample the number of projectiles is less

than 6). At some point, an extremely violent episode starts, including a major military operation,

which may lead to up to 1,315 barrages of projectiles being launched from Gaza together with up

to 2,291 barrages of airstrikes by the IAF.10

Figure 4 complements the evidence of Table 1. This figure presents two superimposed his-

tograms. They depict (i) the number of projectiles attacks form Gaza until the first Israeli re-

taliation and, (ii) the number of airstrikes attacks from Israel until the first Gazan retaliation.

The figure displays a very clear pattern. Gazans react immediately to Israeli airstrikes whereas

Israel shows more patience and restraint on their reactions to Gazan attacks. Accordingly, Gazans

retaliate within two Israeli airstrikes in 21 out of the 28 episodes of violence that start with an

Israeli airstrike; there isn’t any Gazan retaliation for the remainder 7 episodes started by Israeli

violence (this corresponds to the 2.2% of episodes with only Israeli violence reported in Panel B

of Table 1). In contrast, Israel doesn’t retaliate in 183 out of the 284 episodes of violence started

with Gazan’s attacks (this corresponds to 58.7% of episodes with only Gazan militants violence

reported in Panel B of Table 1). For the remainder 101 episodes, Israel retaliates with an airstrike

within two projectiles attacks only for 50% of them.

The final panel of Table 1 shows summary statistics on tahdiya, periods of complete calm in

between violent episodes. These periods are short lived. Half of them last less than 3.4 days and

10A barrage of projectiles includes up to 5 projectiles launched at the same time. A barrage of airstrikes includes

up to 3 airstrikes that occurred simultaneously. For example, the 2,291 barrages of airstrikes reported in the table

during operation Protective Edge in July and August of 2014 correspond to 5,551 airstrikes. The 1,315 projectiles

launched from Gaza during that operation correspond to 1,326 mortars and 4,607 rockets.

8

75% of them last less than 5.3 days. That said, there was a period of over two months without any

projectile or airstrike being launched. This period started on December 23rd, 2012 and lasted until

February 23rd, 2013. This period of calm occurred a month after the ending of Pillar of Defense, a

major military operation, and during the Israeli parliamentary elections of 2013 (voting took place

on January 22nd, 2013). Probably, the duration of this period of calm was also affected by the

inauguration of Obama’s second term as president of the US.

Column (2) in Table 1 presents summary statistics when we remove mortars from the sample.

This brings about a slight increase on the number of violent episodes because we now consider

days with only mortar attacks as days of calm. In addition, eliminating mortars from the analysis

shortens the duration of violent episodes and, obviously, the number of attacks from Gazan mili-

tants. That said, even when we don’t take mortar launches into account we still observe that most

episodes of violence are started and ended by Gazan militants, and over 52% of them only include

Gazan militant violence without any Israeli attack. Therefore, even when we exclude mortars we

do not observe a cycle of violence between episodes.

Columns (3)-(4) and (5)-(6) redefine violent episodes using more stringent requirements of 7

and 14 days of calm, respectively. These columns show that the main results presented in the first

two columns are qualitative and quantitative robust to alternative definitions of violent episodes.

In particular, we continue to find that (i) Gazan militants overwhelmingly start and end violent

episodes; and (ii) in a substantial share of violent episodes we only observe Gazan militants violence.

4. Cycles of Violence

We now shift our focus to intra-episode cycles of violence. Within a violent episode, we say that a

cycle of violence occurs if we observe at least a counter-retaliation to the retaliation. For example,

neither a single rocket attack, nor a rocket attack answered only by an airstrike, are enough to

constitute a cycle of violence. For a cycle of violence to occur, we require an attack followed by

a retaliation which is itself followed by a counter-retaliation. We define the length of a cycle of

violence as the number of alternating attacks. That is, the length of a cycle of violence includes the

initial attack and all subsequent attacks that could be construed as retaliations; i.e. the number of

times that the perpetrator of violence changes sides within an episode plus the initial attack.

Consider, for example, an episode documented by the UN, beginning on November 15th, 2010

9

and ending four days later. The episode begins after dark at 11:15 PM, when unidentified Gazan

militants fire a rocket at the Israeli border town of Sderot. Over the next four days six more

rocket attacks and four mortar barrages are carried out, the last of these occurring at 1:50 PM

on the afternoon of November 19th. We classify all projectile launches from November 15th until

November 19th as part of the same episode because there aren’t two days of calm between these

attacks. Finally, at 3:15 PM on the afternoon of November 19th, the Israeli Air Force (IAF) bombs

a house under construction in the Deir al Balah area, potentially in response to the projectile

fire. Additional airstrikes follow five and fifteen minutes later, at least one of them targeting a

Palestinian Islamic Jihad (PIJ) training base west of Khan Younis Camp. Up until this point,

we have not yet witnessed a cycle of violence. As far as we know, five days of sustained rocket

and mortar attacks on southern Israel have provoked an Israeli reprisal of three airstrikes. This is

consistent with a logic of deterrence. But does it provoke blowback?

Later on the evening of November 19th at 7:25 PM, militants appear to respond to the af-

ternoon’s airstrikes with a rocket launch from Nuseirat Camp. We are now witnessing a cycle of

violence, in the sense that the Israeli reprisal in the afternoon has apparently provoked a counter-

reprisal by Gazan militants. Incidentally, the rocket explodes in mid-air. Nevertheless, a few hours

later at 11:30 PM, the IAF fires two missiles at smuggling tunnels near Rafah Crossing, as if to

counter the counter-reprisal. Finally, Gazan militants strike back at 5:30 AM with a mortar barrage

aimed at the Israeli military base adjacent to the border town of Kissufem. This concludes this

violent episode, as the next violent attack occurs nearly a week later on November 25th. Since we

witnessed three counter-reprisals within this episode (two by Gazan militants and one by the Is-

raelis), we code this cycle of violence with a length equal to 5: the initial attack by Gazan militants,

plus the Israeli reprisal, plus three counter-reprisals.

Applying this definition of cycle of violence to all episodes in the dataset, we calculate the

length of each cyclical violent episode. The results are summarized in Table 2. Consistent with the

definitions we used in Table 1, Columns (1)-(2) use a ‘2 days of calm’ threshold to define episodes

of violence. Columns (3)-(4) use a ‘7 days of calm’ threshold, whereas Columns (5)-(6) use a ‘14

days of calm’ threshold to classify violent episodes.

Let us focus first on Column 1. This column shows that less than 30% of violent episodes have

a cycle of violence (93 out of 312 violent episodes). Other than that, cyclical episodes of violence

and non-cyclical episodes of violence are very similar. Cyclical episodes of violence (i) tend to be

10

short lived, though a little longer than non-cyclical episodes. Fifty percent of them last less than

6.8 days and have a length of less than 5 alternating attacks; (ii) are mostly started and ended by

Gazan violence; (iii) show a great deal of variation in terms of their level of violence; (iv) perhaps

surprisingly, do not lead to substantially long periods of calm in their aftermath.

Result (iv) implies that cycles of violence do not deter future violent attacks for longer period

of times compared to non-cyclical episodes. As supportive evidence, an histogram on the number

of attacks until the first retaliation restricted to cyclical episodes only is very similar to Figure

4.11 Accordingly, Gazan militants react immediately to any Israeli aggression (at most after the

second Israeli attack), whereas Israelis may even wait over 10 Gazan attacks before retaliating (if at

all). Therefore, the evidence shows that Israeli retaliations to Gazan violence do not deter further

attacks within or between violent episodes. Furthermore, Israeli retaliations do not seem to lead to

the de-escalation of violence, at least in terms of the type of projectiles being launched by Gazan

militants. The probability that Gazan militants launch a rocket (compared to mortars which have

a shorter range) within a violent cycle does not seem to be affected by previous Israeli airstrikes.

In addition, after a cyclical episode Gazan militants wait on average only 6 days to launch a Grad

rocket and 4.1 days to launch a Qassam rocket, whereas they wait on average 34.6 days to launch

a Grad rocket and 5.67 days to launch a Qassam rocket after a non-cyclical episode.

To sum up, similar to non-cyclical episodes of violence, the typical cyclical episode of violence

lasts for a week, includes around 12 projectiles launched from Gaza and 4 airstrikes by the IAF, and

is followed by 3 days of calm. This is the case also if we don’t take mortar launches into account

(Column 2). When we focus on Columns 3-4 or 5-6 instead, based on a 7 or 14 days of calm

threshold, respectively, the main message is that violent cyclical episodes last longer, but still don’t

have a long lasting deterrence effect on future attacks. After cycles of violence, we observe a period

of calm that tends to last only a little over a week in Columns 3-4, and a little bit over 20 days

in Columns 5-6. That said, periods of calm after cyclical episodes tend to be shorter than periods

of calm after non-cyclical violent episodes. Therefore, regardless of the threshold chosen for days

of calm between violent episodes, we observe that cyclical episodes of violence are overwhelming

started and ended with Gazan violence, and do not lead to extended periods of calm after they end

vis-a-vis non-cyclical episodes of violence.

11This histogram is available from the authors upon request.

11

5. Impulse Response Functions and VAR Analysis

This section replicates the impulse response functions and VAR analyses of Jaeger and Paserman

(2008) and Haushofer et al. (2010) using our data and time period. Following Jaeger and Paserman

(2008) and Haushofer at al. (2010) we also focus on the daily level (or incidence) of projectiles and

airstrikes attacks. We perform these analyses to demonstrate that the conclusions we reach in the

section above are not a consequence of using a different data or focusing on a different time period.

We first compute nonparametric impulse response functions for the levels and incidences of

projectiles and airstrikes using the same methodology proposed by Jaeger and Paserman (2008).

Following Jaeger and Paserman (2008), we define the Israeli impulse response function as

IsrRFt =

(∑s:Is>0 Is∑s:Is>0 1

)−1(∑s:Is−t>0Gs∑s:Is−t>0 1

−∑

sGs

T

),

where Is is the number of Israeli airstrikes on day s and Gs is the number of projectiles launched

from Gaza on day s. Similarly, Gazan militants’ impulse response function is given by

GazRFt =

(∑s:Gs>0Gs∑s:Gs>0 1

)−1(∑s:Gs−t>0 Is∑s:Gs−t>0 1

−∑

s IsT

).

As pointed out by Jaeger and Paserman (2008), the empirical Israeli response function shows

the excess number of Israeli airstrikes t days after a projectiles attack from Gaza. Analogously, the

empirical Gazan response function depicts the excess number of projectiles launched t days after an

Israeli airstrike. Following Haushofer et al. (2010) we also calculate impulse response functions for

the incidences of airstrikes and projectiles attacks. They have a similar interpretation, but depict

the excess probability of attacks instead of excess in the number of attacks.

Figures 5 and 6 present the impulse response functions for levels of airstrikes and projectiles

attacks, whereas Figures 7 and 8 present the impulse response functions for incidences of airstrikes

and projectiles attacks. All impulse response functions include their respective 95 percent confidence

bands.

All figures show that Israelis and Gazans react in a significant and positive way to an attack by

the other side. Figure 5 suggests that the Israeli Air Force reacts immediately to projectiles attacks.

Accordingly, the excess number of airstrikes against Gaza’s targets significantly increases after a

projectile attack, and remains positive and statistically different from zero for roughly a month after

an attack. Figure 6 depicts the analogous reaction function for Gazan militants. It shows that the

12

initial excess number of projectiles attacks after an airstrike is positive and statistically different

from zero. Moreover, the increase in the excess number of projectile attacks remains statistically

different from zero for almost 50 days. Figures 7 and 8 lead us to the same conclusion while looking

at the excess probability of retaliations.

Together, these figures suggest that Israel and Hamas are locked in an endless cycle of violence,

where both sides react in a regular and predictable way to violence against them. That is, one

side’s attacks are always followed by the other side’s retaliations. These conclusions are consistent

with the results of Haushofer et al. (2010).

Following Jaeger and Paserman (2008) and Haushofer et al. (2010), we estimate a standard

VAR model using daily indicators of projectiles and airstrike attacks to quantify the findings of

Figures 5-8. The models regress daily current Israeli airstrikes and Gazan projectiles launches on

lagged values of both variables. As in Jaeger and Paserman (2008) and Haushofer et al. (2010), our

models also include 14 lags of both variables, which is 4 more lags than the amount recommended

by various information criteria (AIC, HQ, SC, FPE).12 Note also that all four time series pass the

Dickey-Fuller cointegration test.

The results of these analyses are reported in Table 3. For expositional purposes, this table

shows only the F -statistics and p-values for the joint effect of lagged attacks (or incidents) from

the rival side.13 For example, the F -statistic in the first row of column (1) (i.e., the basic model)

tests whether or not all lagged airstrikes before day t affect the number of projectiles launched

on day t. Similarly, the F -statistic in the first row of column (3) tests whether or not all lagged

projectiles launched before day t affect the number of Israeli airstrikes on day t. Columns (2) and

(4) perform the same analyses but focusing on the incidence of attacks instead of the number of

attacks. The bottom panel of Table 3 includes also as a control variable the number of attacks (or

incidence of attacks) by the other side that occurred on day t.

Table 3 shows a very clear and robust pattern whereby past Israeli airstrikes provoke Gazan’s

attacks, and past Gazan’s attacks provoke Israeli airstrikes. In other words, the results of the VAR

analyses suggest that Israel retaliates to Gazan violence and Gazan militants retaliate to Israeli

12The results of our analyses are robust to including only 10 lags of both variables. We choose to present the results

using 14 lags to directly replicate the analyses of Jaeger and Paserman (2008) and Haushofer et al. (2010).13The estimated marginal effects for each lagged variable included in the regressions are available from the authors

upon request.

13

violence. This empirical evidence may lead us to suggest that Israel and Gaza are locked in a vicious

cycle of violence. These results are robust to controlling for attacks on the same day (bottom panel

of Table 3) or to focusing on the incidence of attacks instead of their levels (Columns 2 and 4).

They are also consistent with the impulse response functions depicted in Figures 5-8.

6. Discussion

The results presented in the section above using a VAR analysis point to the existence of a cycle

of violence between Israel and Gazan militants with constant retaliations and counter-retaliations.

However, the evidence presented in Sections 3 and 4 weighs heavily against a cycle-of-violence

narrative for the Israel-Gaza conflict between 2007 and 2014. In particular, we find that exchanges

of attacks between Gaza and Israel tend to be episodic, and that these episodes are not linked to

each other via a provocation and retaliation logic. An overwhelmingly majority of violent episodes

start and end with Gazan attacks. Moreover, a majority of violent episodes consists only of Gazan

militants attacks. We also find that in less than 30% of violent episodes both sides retaliate and/or

counter-retaliate, but these cyclical episodes tend to wrap up fairly quickly.

The different conclusions of the two methodologies highlight the fundamental difference between

an episodic analysis of violence compared to a VAR or VAR-style framework. This leads us to argue

that the VAR methodology is not appropriate for analyses of cycles of violence for a number of

reasons. First, a VAR analysis is able to establish whether or not an attack that occurred on

day t-i may provoke a retaliation on day t. As such, VAR analyses may be able to let us know

that both sides tend to retaliate to violence, but are unable to determine who starts and who

ends violent confrontations. This information is crucial to policy makers trying to stop cycles of

violence. For example, if Israel uses airstrikes only to retaliate to Gazan attacks, forcing Israel to

stop attacking Gaza would not bring an end to violent attacks between the two sides. Moreover,

the VAR methodology is unable to divide cycles of violence into episodic attacks, especially when

these episodes have different durations.

Finally, VAR may generate faulty inference on episodic data generating processes. To show

this, we generate a synthetic dataset where, by construction, the violence is episodic. In particular

we generate data in Python using the following calibration:

• Step 1: On day 1, there is a Gazan projectile attack against Israel with probability 0.135.

14

• Step 2: If there was no attack on day 1, the episode is over, and Python advances to the next

day, returning to Step 1. If there was an attack on day 1, the episode is ongoing, and Israel

retaliates on day 2 with probability 0.342.

• Step 3: If there was no retaliation on day 2, the episode is over, and Python advances to the

next day, returning to Step 1. If there was a retaliation on day 2, Gaza counter-retaliates with

probability 0.663. The episode is now over. Python advances to the next day, and returns to

Step 1.

Following these instructions, Python advances through 2,679 days, which is simply the length

of our UN dataset minus the 61 days corresponding to major military operations. The probabilities

used in the simulation correspond to the conditional probabilities of initiation, retaliation, and

counter-retaliation observed in the UN data. Note that, by construction, the dataset consists of

episodes where both Gaza and Israel only ever retaliate to provocations from the previous day.

We generate 100 datasets in this manner, and run VAR on each one, allowing 7 days of lags.

Reassuringly, VAR correctly finds that Gazan projectiles attacks on day t-1 predict airstrikes on

day t, and likewise, airstrikes on day t-1 predict projectiles on day t. In addition, VAR predicts in

46% of our simulated datasets that airstrikes on t-2 predict projectiles on day t, even though this is

only a spurious correlation by construction. Likewise, airstrikes occurring more than 2 days before

t predict projectiles in day t for 27% of our datasets, and projectiles occurring more than 2 days

before t predict airstrikes in t for 25% of our simulations. These findings show that VAR results

may not be trustworthy when the underlying data generating process is episodic.

7. Conclusions

This paper studies the protracted Gaza-Israeli conflict between 2007 and 2014. The analysis relies

on daily original security reports from the United Nations. A careful analysis of this data set

shows that violent attacks between Israel and Gaza exhibit an episodic pattern, consisting of brief

projectiles and airstrikes skirmishes separated by periods of calm. Most of these episodes of violence

are started and ended by Gazan militants’ attacks, and in a majority of these episodes only Gazan

militants commit attacks. Israel tends to be patient on its retaliation to attacks, even waiting

to five or more projectile attacks before retaliating (if at all). On the contrary, Gazan militants

15

retaliate right after one or two Israeli attacks. Israeli retaliations to Gazan attacks do not seem to

deter or de-escalate future violent attacks.

These results complement previous studies of the Israeli-Palestinian conflict using VAR analyses.

Whereas VAR analyses tend to show that both sides retaliate to violence, the episodic analysis of

this paper clarifies that these retaliations (when they occur) are all intra-episodic. Moreover, the

VAR approach completely ignores three important patterns of this violent conflict: (i) the episodic

nature of the conflict; (ii) Gazan militants tend to start and end episodes of violence; and (iii)

violent episodes are not linked to each other by a pattern of provocation and reprisal. Sure, Israeli

airstrikes do provoke some retaliatory projectile launches in the short term (1-2 days), but once

the episode of violence runs its course, the next period of calm will almost certainly be broken by

a projectile launch unprovoked by bombardment.

Our analysis shows that a VAR analysis does not push the data far enough. The VAR approach

gets snagged on answering the narrower question ‘do both sides retaliate?’ (yes, of course they

do), but when we step back from the trees to see the forest, we recognize the episodic structure

of a conflict that re-ignites over and over again for non-cyclical reasons. Therefore, we encourage

researchers investigating cycles of violence in Israel-Palestine and other conflicts to move beyond

the VAR framework and investigate time series data more creatively.

This paper shows that the main determinants of violence are non-cyclical. These determinants

may lead to Gazan militant’s attacks, where Israel sometimes retaliates to these attacks with

airstrikes and other times shows restraint. A thorough analysis of the non-cyclical determinants of

Gazans’ attacks is beyond the scope of our paper. That said, most of the related literature points

to two main reasons behind Gazan’s attacks: resisting the Israeli blockade of the Gaza Strip and

outbidding the Palestinian Authority for Palestinians’ support.

Israel has maintained strict control of its border with the Gaza Strip at least since it evacuated

its settlements on the summer of 2005. Borders control turned into an Israeli and Egyptian blockade

of the Gaza Strip after Hamas seized government institutions of the Gaza Strip from Fatah in June

2007 (Kershner, 2007).14 The blockade has been associated with the dire performance of the Gazan

economy during the last ten years. Etkes and Zimring (2015), for example, show that the Israel-

Egyptian blockade of Gaza brought about a decrease in the order of 14% to 27% on its residents

14Israel maintains that the blockade of the Gaza Strip is necessary to limit mortar and rocket attacks from the

Gaza Strip, and to prevent Hamas from obtaining more weapons.

16

welfare (as calculated using the household expenditure survey). Moreover, the Israeli-Egyptian

blockade of Gaza is associated with soaring unemployment rates and increasing rates of moderate

and severe food insecurity (UN report, 2016). Given all of the above, the blockade acts as a

longstanding grievance that motivates Gazan militants attacks against Israel.

The second determinant of violence often mentioned in the literature is related to the extant

rivalry between Palestinian militant groups. This rivalry has historically motivated attacks against

Israel as each group seeks to win new recruits, funding, and political power by proving it is more

committed to ’resistance’ than its rival groups (see, e.g., Bloom (2005), Pearlman (2014), Jaeger

et al. (2015), and Krause (2017), among many others). Spoiler and chain-ganging tactics can

therefore generate militant projectile launches even without Israeli provocation.

Thus the Palestinian movement’s internal political group competition, and long-term underlying

grievances against Israel, are likely the main determinants of mortar and rockets attacks. By getting

mixed up in VAR analysis, the cycles-of-violence literature has sidetracked itself into short-term

dynamics and an undue emphasis on short-term motives.

In conclusion, the Israel-Gaza Conflict is not an endless cycle of violence between two bitter

enemies. It is an episodic conflict, and although a minority of episodes are somewhat lengthened

by cyclical violence, the two sides seem to judge each other’s tolerance for reprisals accurately

and de-escalate in short order. Violent episodes themselves are over and over again initiated (and

terminated) by Gazan projectile launches likely motivated by long-term underlying grievances and

internal political calculus between Gazan militant factions. Until the fundamental political issues

between Israelis and Palestinians (and Egyptians) are resolved, we can expect repeated episodes of

violence between Gazan militants and the Israeli government.

References

Berger, Rony, Marc Gelkopf and Yotam Heineberg. 2012. “A Teacher-Delivered Intervention for

Adolescents Exposed to Ongoing and Intense Traumatic War-Related Stress: A Quasi-Randomized

Control Study,” The Journal of Adolescent Health, 51 (5): 453-461.

Bloom, Mia. 2005. Dying to Kill: The Allure of Suicide Terror. New York, NY: Columbia Univer-

sity Press.

Brym, Robert and Bader Araj. 2006. “Suicide Bombings as Strategy and Interaction: The Case

of the Second Intifada,” Social Forces, 84 (4): 1969-1986.

17

Diamond, Gary M., Joshua D. Lipsitz, Zvi Fajerman, and Omit Rozenblat. 2010. “Ongoing Trau-

matic Stress Response (OTSR) in Sderot, Israel,” Professional Psychology: Research and Practice,

41 (1): 19-25.

Dugan, Laura and Erica Chenoweth. 2012.“Moving Beyond Deterrence: The Effectivenes of Rais-

ing the Expected Utility of Abstaining from Terrorism in Israel,” American Sociological Review, 77

(4): 597-624.

Ephron, Dan. 2015. Killing a King: The Assassination of Yitzhak Rabin and the Remaking of

Israel. New York, NY: W.W. Northon and Company, Inc.

Etkes, Haggay and Assaf Zimring. 2015. “When Trade Stops: Lessons from the Gaza Blockade

2007-2010,” Journal of International Economics, 95 (1): 16-27.

Granger, Clive W. J. 1969. “Investigating Causal Relations by Econometric Models and Cross-

Spectral Methods,” Econometrica, 37 (3): 424-438.

Goldberg, Lital, Jacob Dreiher, Michael Friger, Alexander Levin, and Pesach Shvartzman. 2013.

“Health Services Utilization under Qassam Rocket Attacks,” Israeli Medical Association Journal,

15 (8): 482-486.

Houshofer, Johannes, Anat Biletzki and Nancy Kanwisher. 2010. “Both Sides Retaliate in the

Israeli-Palestinian Conflict,” Proceedings of the National Academy of Sciences, 107 (42): 17927-

17932.

Jaeger, David A., Esteban F. Klor, Sami H. Miaari and M. Daniele Paserman. 2015. “Can Mili-

tants Use Violence to Win Public Support? Evidence from the Second Intifada,” Journal of Conflict

Resolution, 59 (3): 528-549.

Jaeger, David A. and M. Daniele Paserman. 2006. “Israel, the Palestinian Factions and the Cycle

of Violence,” The American Economic Review, 96 (2): 45-49.

Jaeger, David A. and M. Daniele Paserman. 2008. “The Cycle of Violence? An Empirical Analysis

of Fatalities in the Palestinian-Israeli Conflict,” The American Economic Review, 98 (4): 1591-1604.

Jaeger, David A. and M. Daniele Paserman. 2009. “The Shape of Things to Come? On the Dy-

namics of Suicide Attacks and Targeted Killings,” The Quarterly Journal of Political Science, 4:

315-342.

Johnson, Chalmers. 2000. Blowback: The Costs and Consequences of American Empire. New

York, NY: Macmillan.

18

Krause, Peter. 2017. Rebel Power: Why National Movements Compete, Fight, and Win. Ithaca,

NY: Cornell University Press.

Kershner, Isabel. 2007. “Abbas’s Premier Tells Israel to Reopen Gaza,” The New York Times,

December 14th.

Knuth, Donald. 1973. The Art of Computer Programming, Volume 3. Boston, MA: Addison-

Wesley.

Pearlman, Wendy. 2014. Violence, Nonviolence, and the Palestinian National Movement. Cam-

bridge: Cambridge University Press.

Schelling, Thomas C. 1966. Arms and Influence. New Haven, CT: Yale University Press.

Sobelman, Daniel. 2017. “Learning to Deter: Deterrence Failure and Success in the Israel-

Hezbollah Conflict, 2006-2016,” International Security, 41 (3): 151-196.

United Nations Office for the Coordination of Humanitarian Affairs (OCHA). 2016. The Gaza

Strip: The Humanitarian Impact of the Blockade, November.

Wainstock, Tamar, Eyal Anteby, Saralee Glasser, Ilana Shoham-Vardi and Liat Lerner-Geva. 2013.

“The Association Between Prenatal Maternal Objective Stress, Perceived Stress, Preterm Birth

and Low Birthweight,” The Journal of Maternal-Fetal Neonatal Medicine, 26 (10): 973-977.

19

Figure 1: Gaza Projectiles and Israeli Airstrikes Attacks, 2007-2014

Note: Using UN data from October 1st, 2006 through December 31st, 2014.

20

Figure 2: Gazan Militants Retaliatory Delays

Note: Using Meir Amit data from April 15th, 2009 through July 1st, 2016.

Figure 3: Israel Air Force Retaliatory Delays

Note: Using Meir Amit data from April 15th, 2009 through July 1st, 2016.

21

Figure 4: Number of Attacks Until First Retaliation

Note: Using UN data from October 1st, 2006 through December 31st, 2014.

22

Figure 5: Israeli Impulse Response Function to Projectiles: Levels

Figure 6: Gaza Impulse Response Function to Airstrikes: Levels

23

Figure 7: Israeli Impulse Response Function to Projectiles: Incidence

Figure 8: Gaza Impulse Response Function to Airstrikes: Incidence

24

Rockets, Missiles

and Mortars

Rockets and

Missiles Only

Rockets, Missiles

and Mortars

Rockets and

Missiles Only

Rockets, Missiles

and Mortars

Rockets and

Missiles Only

(1) (2) (3) (4) (5) (6)

312 316 43 56 11 17

Minimum 0 0 0 0 0 0Median 0.9 0.5 11.5 7.2 55.3 55.3Maximum 129.8 58.3 386.6 374.3 1,403.6 596.5Standard Deviation 10.2 6.6 81.8 62.2 411.7 184.0

Started with Gazan Militants Attack 91.0 87.3 95.3 92.9 100.0 94.1Ended with Gazan Militants Attack 84.9 79.4 81.4 80.4 81.8 88.2With only Gazan Militants' Violence 58.7 52.2 44.2 46.4 36.4 41.2With only Israeli Violence 2.2 4.1 0.0 0.0 0.0 0.0

Minimum 0 0 1 1 1 1Median 2 2 5 4 24 20Maximum 1,315 1,082 1,646 1,334 2,564 1,335Standard Deviation 91.0 69.5 325.1 221.3 881.5 406.9

Minimum 0 0 0 0 0 0Median 0 0 1 1 5 5Maximum 2,291 2,291 2,809 2,809 2,838 2,809Standard Deviation 137.3 136.2 438.6 385.8 871.4 687.5

Minimum 2.0 2.0 7.2 7.0 15.2 14.1Median 3.4 3.7 10.4 11.0 25.9 22.8Maximum 62.2 62.2 62.2 62.2 62.2 62.2Standard Deviation 5.8 6.1 11.4 10.4 13.9 12.9

Table I: Episodes Statistics by Number of Days without Attacks

Number of Days without Attacks at least 2 days at least 7 days at least 14 days

Notes: Calculations in the table use the universe of rockets launches and airstrikes attacks. Data from the UN from June 15, 2007 until December 31, 2014.

E. Number of Days Without Attacks Between Episodes

Number of Episodes

A. Episode Duration (number of days)

B. Percent of Episodes

C. Gazan Militants Violence (number of barrage of attacks)

D. Israeli Violence (number of barrage of attacks)

Rockets, Missiles and

Mortars

Rockets and Missiles

Only

Rockets, Missiles and

Mortars

Rockets and Missiles

Only

Rockets, Missiles and

Mortars

Rockets and Missiles

Only

(1) (2) (3) (4) (5) (6)

312 316 43 56 11 17

93 102 21 26 7 10

70.2 67.7 51.2 53.6 36.4 41.2

Minimum 0.1 0.1 5.4 4.6 14.2 14.2Median 6.8 6.3 70.9 48.9 201.9 168.5Maximum 129.8 58.3 386.6 374.3 1,403.6 596.5Standard Deviation 16.6 9.5 97.7 78.3 482.3 191.0

Started with Gazan Militants Attack 88.2 85.3 95.2 88.5 100 90Ended with Gazan Militants Attacks 76.3 71.6 71.4 69.2 71.4 80

Minimum 3 3 3 3 3 3Median 5 5 20 18.5 91 169.5Maximum 1,516 1,330 1,876 1,630 1,900 1,630Standard Deviation 167.1 140.3 413.2 328.3 724.7 501.8

Minimum 1 1 5 2 5 5Median 12 10 50 33 189 304.5Maximum 1,315 1,082 1,646 1,334 2,564 1,335Standard Deviation 161.1 118.7 430.7 305.2 1,013.1 456.8

Minimum 1 1 1 1 1 1Median 4 5 16 15.5 81 15.5Maximum 2,291 2,291 2,809 2,809 2,838 2,809Standard Deviation 249.0 237.7 614.5 556.4 1,037.8 860.5

Minimum 2.0 2.0 7.2 7.0 15.2 14.1Median 3.1 3.0 9.3 9.2 23.5 20.7Maximum 24.0 24.0 34.6 34.5 34.6 34.6Standard Deviation 2.7 2.7 8.4 6.3 7.7 7.9

Table II: Statistics on Cycles of Violence (by Number of Days without Attacks)

Number of Days without Attacks at least 2 days at least 7 days at least 14 days

Notes: Calculations in the table use the universe of rockets launches and airstrikes attacks. Data from the UN from June 15, 2007 until December 31, 2014.

F. Number of Days Without Attacks After a Cycle

D. Gazan Militants Violence (number of barrage of attacks)

E. Israeli Violence (number of barrage of attacks)

C. Length of Cycles (# of alternating attacks)

Data Source

Number of Episodes

Number of Cycles of Violence

Percent of Episodes without a Cycle

A. Cycles Duration (in number of days)

B. Percent of Cycles of Violence

Number Incidence Number Incidence

Specification Test Statistic (1) (2) (3) (4)

Basic F statistic 34.856*** 5.064*** 5.8957*** 6.2346***

p -value <2.2E-16 8.28E-07 7.23E-09 1.70E-09

Control Same-Day Events F statistic 253.5*** 22.537*** 206.18*** 22.144***

p -value < 2.2E-16 < 2.2E-16 <2.2E-16 <2.2E-16

Table III: Gaza Projectile and Airstrike Retaliations

Gaza Projectiles Retaliating to Airstrikes

Airstrikes retaliating to Gaza Projectiles

Note: F- statistic and respective p -value test for the joint significance of the lagged coefficients of the respective other variable.

Appendix Figures and Tables:

Figure A1: Flowchart of Data Generation

Figure A2: Illustration of Python Automated Grammar Parsing